Import Question JSON

Current Question (ID: 11071)

Question:

$\text{An insulator container contains 4 moles of an ideal diatomic gas at a temperature T. If heat Q is supplied to this gas, due to which 2 moles of the gas are dissociated into atoms, but the temperature of the gas remains constant, then:}$

Options:

1. $Q = 2RT$
2. $Q = RT$ (Correct)
3. $Q = 3RT$
4. $Q = 4RT$

Solution:

$Q = \Delta U = U_f - U_i = [\text{internal energy of 4 moles of a monoatomic gas + internal energy of 2 moles of a diatomic gas}] - [\text{internal energy of 4 moles of a diatomic gas}]$ $= \left(4 \times \frac{3}{2} RT + 2 \times \frac{5}{2} RT\right) - \left(4 \times \frac{5}{2} RT\right) = RT$ $= RT$ $\text{Note: (1) 2 moles of diatomic gas become 4 moles of a monoatomic gas when gas is dissociated into atoms.}$ $\text{(2) Internal energy of } \mu \text{ moles of an ideal gas of degrees of freedom F is given by: } U = \frac{F}{2} \mu RT$ $f = 3 \text{ for a monoatomic gas and } 5 \text{ for diatomic gas.}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}